Question: Simplify the following expression: $q = \dfrac{-6p^2 + 54p - 108}{p - 6} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ q =\dfrac{-6(p^2 - 9p + 18)}{p - 6} $ Then we factor the remaining polynomial: $p^2 {-9}p + {18} $ ${-6} {-3} = {-9}$ ${-6} \times {-3} = {18}$ $ (p {-6}) (p {-3}) $ This gives us a factored expression: $\dfrac{-6(p {-6}) (p {-3})}{p - 6}$ We can divide the numerator and denominator by $(p + 6)$ on condition that $p \neq 6$ Therefore $q = -6(p - 3); p \neq 6$